$a_n={\dfrac{n-2}{(n+1)!}}$ 1) Find $\lim_{n\to\infty}\left| \dfrac{a_{n+1}}{a_n} \right|$. $\lim_{n\to\infty}\left|\, \frac{{{a}_{n+1}}}{{{a}_{n}}} \,\right|=$
Answer: $\lim_{n\to\infty}\left| \,\frac{{{a}_{n+1}}}{{{a}_{n}}}\, \right|=0$ Since the limit, $0$, is less than $1$, the ratio test tells us that the series converges.